A215049 Number of primes of the form 1 + b^8 for 1 < b < 10^n.

2, 2, 40, 335, 2498, 20886, 174368, 1507722, 13300713

Offset: 1

Author

Henryk Dabrowski, Aug 01 2012

Keywords

• nonn

Comments

Primes 1 + b^8 are a form of generalized Fermat primes. It is conjectured that a(n) is asymptotic to 0.261599*li(10^n).

Examples

			a(1) = 2 because the only Fermat primes F_3(b) where b<10^1 are the primes: 257, 65537.
		

Links

• Yves Gallot, Status of the smallest base values yielding Generalized Fermat primes
• Yves Gallot, How many prime numbers appear in a sequence ?
• Yves Gallot, A Problem on the Conjecture Concerning the Distribution of Generalized Fermat Prime numbers (a new method for the search for large primes)

Crossrefs

Cf. A214454.

Programs

Mathematica

Table[Length[Select[Range[2,10^n-1]^8 + 1, PrimeQ]], {n, 5}] (* T. D. Noe, Aug 01 2012 *)

PARI

a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^8+1))

Formula

a(n) = A214454(8*n) - 1.